LinearDependence(S, R)ΒΆ

lindep.spad line 1

Test for linear dependence.

linearDependence: Vector R -> Union(Vector S, failed)
linearDependence([v1, ..., vn]) returns [c1, ..., cn] if c1*v1 + ... + cn*vn = 0 and not all the ci's are 0, “failed” if the vi's are linearly independent over S.
linearlyDependent?: Vector R -> Boolean
linearlyDependent?([v1, ..., vn]) returns true if the vi's are linearly dependent over S, false otherwise.
particularSolution: (Matrix R, Vector R) -> Union(Vector Fraction S, failed) if S hasn’t Field
particularSolution([v1, ..., vn], u) returns [c1, ..., cn] such that c1*v1 + ... + cn*vn = u, “failed” if no such ci's exist in the quotient field of S.
particularSolution: (Matrix R, Vector R) -> Union(Vector S, failed) if S has Field
particularSolution([v1, ..., vn], u) returns [c1, ..., cn] such that c1*v1 + ... + cn*vn = u, “failed” if no such ci's exist in S.
particularSolution: (Vector R, R) -> Union(Vector Fraction S, failed) if S hasn’t Field
particularSolution([v1, ..., vn], u) returns [c1, ..., cn] such that c1*v1 + ... + cn*vn = u, “failed” if no such ci's exist in the quotient field of S.
particularSolution: (Vector R, R) -> Union(Vector S, failed) if S has Field
particularSolution([v1, ..., vn], u) returns [c1, ..., cn] such that c1*v1 + ... + cn*vn = u, “failed” if no such ci's exist in S.
solveLinear: (Matrix R, Vector R) -> Record(particular: Union(Vector Fraction S, failed), basis: List Vector Fraction S) if S hasn’t Field
solveLinear([v1, ..., vn], u) returns solution of the system c1*v1 + ... + cn*vn = u and and a basis of the associated homogeneous system c1*v1 + ... + cn*vn = 0
solveLinear: (Matrix R, Vector R) -> Record(particular: Union(Vector S, failed), basis: List Vector S) if S has Field
solveLinear([v1, ..., vn], u) returns solution of the system c1*v1 + ... + cn*vn = u and and a basis of the associated homogeneous system c1*v1 + ... + cn*vn = 0
solveLinear: (Vector R, R) -> Record(particular: Union(Vector Fraction S, failed), basis: List Vector Fraction S) if S hasn’t Field
solveLinear([v1, ..., vn], u) returns solution of the system c1*v1 + ... + cn*vn = u and and a basis of the associated homogeneous system c1*v1 + ... + cn*vn = 0
solveLinear: (Vector R, R) -> Record(particular: Union(Vector S, failed), basis: List Vector S) if S has Field
solveLinear([v1, ..., vn], u) returns solution of the system c1*v1 + ... + cn*vn = u and and a basis of the associated homogeneous system c1*v1 + ... + cn*vn = 0